Conditions for rings to be finite or have only central zero divisors

Abraham A. Klein; Howard E. Bell

doi:10.1556/SScMath.2007.1019

Conditions for rings to be finite or have only central zero divisors

Abraham A. Klein^*
, Howard E. Bell

^*Corresponding author for this work

School of Mathematical Sciences

Brock University

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We characterize rings having only finitely many noncentral subrings of zero divisors, and rings in which every proper noncentral subring of zero divisors is finite.

Original language	English
Pages (from-to)	291-296
Number of pages	6
Journal	Studia Scientiarum Mathematicarum Hungarica
Volume	44
Issue number	2
DOIs	https://doi.org/10.1556/SScMath.2007.1019
State	Published - Apr 2007

Keywords

Commutator ideal
Noetherian ring
Non-central subring of zero divisors
Periodic ring
Unique factorization domain

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10.1556/SScMath.2007.1019

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title = "Conditions for rings to be finite or have only central zero divisors",

abstract = "We characterize rings having only finitely many noncentral subrings of zero divisors, and rings in which every proper noncentral subring of zero divisors is finite.",

keywords = "Commutator ideal, Noetherian ring, Non-central subring of zero divisors, Periodic ring, Unique factorization domain",

author = "Klein, \{Abraham A.\} and Bell, \{Howard E.\}",

year = "2007",

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doi = "10.1556/SScMath.2007.1019",

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AU - Klein, Abraham A.

AU - Bell, Howard E.

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AB - We characterize rings having only finitely many noncentral subrings of zero divisors, and rings in which every proper noncentral subring of zero divisors is finite.

KW - Commutator ideal

KW - Noetherian ring

KW - Non-central subring of zero divisors

KW - Periodic ring

KW - Unique factorization domain

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JO - Studia Scientiarum Mathematicarum Hungarica

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IS - 2

ER -

Conditions for rings to be finite or have only central zero divisors

Abstract

Keywords

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